Question

\(\sin(90^\circ - A) = \)

• A. \(\sin A\)
• B. \(\cos A\)
• C. \(\tan A\)
• D. \(\sec A\)

Hint:

Remember the main pairs of complementary identities: \(\sin(90^\circ - A) = \cos A\), \(\cos(90^\circ - A) = \sin A\), and \(\tan(90^\circ - A) = \cot A\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests the knowledge of fundamental trigonometric identities, specifically the complementary angle identities.

Step 2: Key Formula or Approach:
The complementary angle identities state the relationship between trigonometric functions of an angle and its complement (90° minus the angle). The key identity here is:
\[ \sin(90^\circ - A) = \cos A \]

Step 3: Detailed Explanation:
This is a direct application of the identity. The sine of an angle is equal to the cosine of its complementary angle. Therefore, \(\sin(90^\circ - A)\) is equal to \(\cos A\).

Step 4: Final Answer:
The value of \(\sin(90^\circ - A)\) is \(\cos A\).